Finite Group Databasebeta

← #14647417

Subgroups — #14647417

Order 2816.

310 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068303C211yesmaximal, characteristic
2#13067362C212yesmaximal
3#13066460C212yesmaximal
4#13066445C211yesmaximal, characteristic
5C11×#1274C211yesmaximal, characteristic
6C11×#431C2212yes—
7C11×#376C2211yescharacteristic
8#10622538C2212yes—
9C2×#66867C411yescharacteristic
10C2×#66867C411yescharacteristic
11C2×#66867C2211yescharacteristic
12C2×C4×C11⋊C8C411yescharacteristic
13C2×C4×C11⋊C8C411yescharacteristic
14C2×C4×C11⋊C8C2211yescharacteristic
15#10622118—22no—
16#10622117—22no—
17C2×C42×C11C2×C411yescharacteristic
18C2×C42×C11C2×C411yescharacteristic
19C2×C42×C11C2311yescharacteristic
20C22×C11⋊C8C2×C411yescharacteristic
21C22×C11⋊C8C2×C411yescharacteristic
22C22×C11⋊C8C2×C411yescharacteristic
23C22×C11⋊C8C2×C411yescharacteristic
24C11×C4⋊C8—22no—
25C11×C22⋊C8—22no—
26C4×C8×C11—22no—
27C11×#95—22no—
28C22⋊(C11⋊C8)—22no—
29C4⋊(C11⋊C8)—22no—
30#66867—22no—
31#66867—22no—
32#66867—22no—
33C4×C11⋊C8—22no—
34C4×C11⋊C8—22no—
35C4×C11⋊C8C814yescomplemented
36C4×C11⋊C8D411yescharacteristic
37C4×C11⋊C8D411yescharacteristic
38C4×C11⋊C8Q811yescharacteristic
39C4×C11⋊C8Q811yescharacteristic
40#8780—111nomaximal, Sylow
41C22×C4×C11—21no—
42C22×C4×C11—21no—
43C22×C4×C11C22×C411yescharacteristic
44C22×C4×C11#4112yes—
45C2×C8×C11—42no—
46C42×C11—21no—
47C42×C11—21no—
48C42×C11C2×C812yes—
49C42×C11M1612yes—
50C42×C11C2×D411yescharacteristic
51C42×C11C2×Q811yescharacteristic
52C42×C11#4112yes—
53C2×C11⋊C8—21no—
54C2×C11⋊C8—21no—
55C2×C11⋊C8—21no—
56C2×C11⋊C8—21no—
57C2×C11⋊C8—21no—
58C2×C11⋊C8—21no—
59C2×C11⋊C8—42no—
60C2×C11⋊C8C4⋊C411yescharacteristic
61C2×C11⋊C8C4⋊C411yescharacteristic
62C2×C11⋊C8C4⋊C411yescharacteristic
63C2×C11⋊C8C4⋊C411yescharacteristic
64C2×C11⋊C8C2×C812yes—
65C2×C11⋊C8C2×C812yes—
66C2×C11⋊C8M1612yes—
67C2×C11⋊C8M1612yes—
68#1726—111no—
69#1564—112no—
70#1281—112no—
71#1274—111no—
72#1274D1111yescharacteristic
73C23×C11#11711yescharacteristic
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—42no—
77C2×C4×C11—42no—
78C2×C4×C11—42no—
79C2×C4×C11C2×C4⋊C411yescharacteristic
80C2×C4×C11#11711yescharacteristic
81C2×C4×C11#12412yes—
82C2×C4×C11#12512yes—
83C2×C4×C11C22×C811yescharacteristic
84C2×C4×C11C2×M1611yescharacteristic
85C2×C4×C11C2×M1611yescharacteristic
86C2×C4×C11C2×M1611yescharacteristic
87C8×C11—82no—
88C11⋊C8—21no—
89C11⋊C8—21no—
90C11⋊C8—22no—
91C11⋊C8—22no—
92C11⋊C8—82no—
93C11⋊C8C4⋊C812yes—
94C11⋊C8C4⋊C812yes—
95#431—112no—
96#431C2×D1112yes—
97C2×#97—111no—
98C2×#97—111no—
99C2×#97—111no—
100C2×C4×C8—111no—
101C2×C4×C8—111no—
102C2×C4×C8—111no—
103#376C2×D1111yescharacteristic
104#335—222no—
105#334—222no—
106C22×C11—22no—
107C22×C11#38211yescharacteristic
108C22×C11#43111yescharacteristic
109C22×C11#43211yescharacteristic
110C4×C11—22no—
111C4×C11—22no—
112C4×C11—42no—
113C4×C11—42no—
114C4×C11C2×C4⋊C811yescharacteristic
115C4×C11#42311yescharacteristic
116C4×C11#43111yescharacteristic
117C4×C11#43211yescharacteristic
118C22×C8—111no—
119C22×C8—111no—
120C22×C8—111no—
121C22×C8—111no—
122C2×C42C4×D1111yescharacteristic
123C2×C42C4×D1111yescharacteristic
124C2×C42C22×D1111yescharacteristic
125C4⋊C8—22no—
126C4⋊C8—222no—
127C22⋊C8—22no—
128C22⋊C8—222no—
129#97—222no—
130#97—222no—
131#97—222no—
132C4×C8—22no—
133C4×C8—114no—
134C4×C8—111no—
135C4×C8—111no—
136C4×C8—111no—
137C4×C8—111no—
138C4×C8—222no—
139C4×C8—222no—
140#95—22no—
141C2×C11—21no—
142C2×C11—21no—
143C2×C11#183111yescharacteristic
144C2×C11#183312yes—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4C2×C4×D1111yescharacteristic
148C22×C4#434112yes—
149C2×C8—42no—
150C2×C8—111no—
151C2×C8—111no—
152C2×C8—112no—
153C2×C8—112no—
154C2×C8—111no—
155C2×C8—111no—
156C2×C8—112no—
157C2×C8—112no—
158C2×C8—221no—
159C2×C8—221no—
160C2×C8—221no—
161C2×C8—221no—
162C2×C8—221no—
163C2×C8—221no—
164C2×C8—442no—
165C42—21no—
166C42—21no—
167C42C8×D1112yes—
168C42#431312yes—
169C42#433912yes—
170C42D4×D1111yescharacteristic
171C42Q8×D1111yescharacteristic
172C11#878011yescharacteristic, complemented, Sylow
173C23#6693011yescharacteristic
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4#6692511yescharacteristic
180C2×C4#6693812yes—
181C2×C4#6694212yes—
182C2×C4C4⋊C4×D1111yescharacteristic
183C2×C4C2×C8×D1111yescharacteristic
184C2×C4C2×#431311yescharacteristic
185C2×C4M16×D1111yescharacteristic
186C2×C4M16×D1111yescharacteristic
187C8—82no—
188C8—112no—
189C8—112no—
190C8—222no—
191C8—222no—
192C8—221no—
193C8—221no—
194C8—882no—
195C22—22no—
196C22#1062226311yescharacteristic
197C22#1062233111yescharacteristic
198C22#1062233211yescharacteristic
199C4—22no—
200C4—22no—
201C4—42no—
202C4—42no—
203C4#1062229811yescharacteristic
204C4#1062231811yescharacteristic
205C4D11×C4⋊C811yescharacteristic
206C4#1062245011yescharacteristic
207C2—21no—
208C2—21no—
209C2#1306873111yescharacteristic
210C2#1306873812yes—
subgroupG/H
centerC2×C4#66925
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC11×#1274C2
socleC22×C11#382
prime radicalC23×C11#117
cosocleC2×C42×C11C23
hypercenter#1274D11
hypocenterC11#8780
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #376 ◁ #1274

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
35. C4×C11⋊C8C8semidirect
172. C11#8780semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130683032
#130673622
#130664602
#130664452
C11×#12742
#878011